Numerade

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The normalization condition for a three-dimensional wave function is . (a) Show that in spherical polar coordinates, the element of volume is dV = r^2drsin(theta)d(theta)d(phi). [Hint: Think about the infinitesimal volume between r and r + dr, between (theta) and (theta) + d(theta), and between (phi) and (phi) + d(phi).] (b) Show that if (psi) = R(r)Y((theta), (phi)), the normalization integral is the product of two terms

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7. The transmission le below represents a distribution le and load that has been shorted at its end. Calculate the input impedance at a distance of 0.35? to the left of the load. Zo-50? ZL-500 0.35?

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The relative frequency of rates less than 120 using the 68-95-99.7 rule is

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In the problems below, G = (V, E) is an undirected graph on n vertices and m edges, and assume m ? n. a. A matching M is a subset of edges which don't share endpoints. Suppose G has a matching M of size n/2, that is, it's a perfect matching. You sample a subset R ? V where every vertex v is independently present in R with probability $p := \frac{s}{n}$. What is the smallest value of s, as a function of n, such that the probability that R contains both the endpoints of some edge in M is at least 50%? Clearly show your work explaining your reasoning.

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A major reason why sexually transmitted diseases are passed so easily is that in many instances, people know they are infected. Group of answer choices True False

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Dopamine neurons respond to an error in prediction No predictions Reward occurs Reward predicted Reward occurs Reward predicted No reward occurs (no CS) R a b CS R C -1 CS 0 1 2s (no R) Schultz, W. (1998), Figure 2 from "Predictive reward signal of dopamine neurons." Journal of Neurophysiology, 80(1), 1-27. Copyright © 1993 by American Physiological Society. Reproduced with permission of American Physiological Society in the format Textbook via Copyright Clearance Center.

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PROBLEM 2 - Suppose you release a 2kg mass on a frictionless inclined plane from rest, and the mass slides 4m along the plane. What is the final velocity of the mass? Start by drawing a diagram.

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Evaluate the integral $ \int 1 \sin^3(x) \sqrt{\cos(x)} \, dx $, $ -\pi/2 \le x \le \pi/2 $ Note: Use an upper-case \"C\" for the constant of integration.

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The blending inheritance hypothesis proposed that the genetic material from parents is mixed in the offspring. As a result, traits of offspring and later descendants should lie between the phenotypes of parents. Mendel, in contrast, proposed that genes are discrete and that their integrity is maintained in the offspring and in subsequent generations. Suppose the year is 1890. You are a horse breeder who has just read Mendel's paper. You don't believe his results, however, because you often work with cremello (very light-colored) and chestnut (reddish-brown) horses. You know that when you breed a cremello individual from a pure-breeding line with a chestnut individual from a pure-breeding line, the offspring are palomino − meaning they have an intermediate (golden-yellow) body color.

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Q2. Write the type of carbonyl condensation reaction in each of the following reactions. (4 marks) OH O NaOH R ethanol R NaOH R ethanol R R R 1. NaOR RRRR R 2. H,O NaOR ethanol HH R O-R+ HOR

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miriam g.